Question

find angle c in this equilateral triangle.

\\(a = 60^{\circ}\\) and \\(b = 60^{\circ}\\)

Explanation:

🆕 New Concept Discovered: Triangle Angle Sum Theorem
The interior angles of any triangle always add up to \( 180^\circ \).

Step 1: Identify the given values

We are given the measures of two angles in the triangle:

$$ A = 60^\circ $$

$$ B = 60^\circ $$

Step 2: Apply the Triangle Angle Sum Theorem

The sum of all interior angles in any triangle is always \( 180^\circ \):

$$ A + B + C = 180^\circ $$

Substitute the known values into the equation:

$$ 60^\circ + 60^\circ + C = 180^\circ $$

Step 3: Solve for angle C

Combine the known angles:

$$ 120^\circ + C = 180^\circ $$

Subtract \( 120^\circ \) from both sides to find \( C \):

$$ C = 180^\circ - 120^\circ $$

$$ C = 60^\circ $$

(Note: In an equilateral triangle, all three sides are equal, and all three interior angles are always equal to \( 60^\circ \).)

Answer:

60